With the advancement of circuit design complexity and technology nodes, buffer insertion has become pivotal in mitigating timing violations, significantly impacting the physical design development cycle and highlighting the necessity for acceleration methodologies. In this paper, we present BIGX, a GPU-accelerated algorithmic framework for buffer insertion. BIGX is versatile and can be adapted to implement different dynamic programming (DP) based buffering algorithms for repairing various types of timing violations. In particular, we introduce MCDP, a dedicated DP-based buffering algorithm for repairing maximum capacitance violations, and propose a parallel version of Van Ginneken’s algorithm for setup violations, both algorithms are incorporated and implemented in BIGX. Furthermore, to overcome the runtime limitations of DP-based buffering algorithms, BIGX adopts a distributed Branch Merge algorithm based on bucket sorting, which fully leverages the hierarchical memory architecture of modern GPUs to achieve substantial speedups while preserving solution quality. Experimental results on industrial benchmarks demonstrate that, with the integration of MCDP, BIGX repairs 96.6% of maximum capacitance violations. Compared to OpenROAD, BIGX with MCDP repairs 2.54x more maximum capacitance violations and delivers a 3.37x speedup. Additionally, BIGX accelerates the Van Ginneken’s algorithm by 11.68x while maintaining comparable solution quality to its CPU-based counterpart.